# 9.3 - Lesson 9 Summary

## Objectives

Upon successful completion of this lesson, you should be able to:

• Identify situations in which the z or t distribution may be used to approximate a sampling distribution
• Construct a confidence interval to estimate the difference in two population proportions and two population means using Minitab Express given summary or raw data
• Conduct a hypothesis test for two proportions and two means using Minitab Express given summary or raw data
Confidence Interval Test Statistic $$(\widehat{p}_1-\widehat{p}_2) \pm z^\ast {\sqrt{\frac{\widehat{p}_1 (1-\widehat{p}_1)}{n_1}+\frac{\widehat{p}_2 (1-\widehat{p}_2)}{n_2}}}$$ $$z=\frac{\widehat{p}_1-\widehat{p}_2}{\sqrt{\widehat{p}(1-\widehat{p})\left ( \frac{1}{n_1}+\frac{1}{n_2} \right )}}$$ $$(\bar{x}_1-\bar{x}_2) \pm t^\ast{ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$ $$Estimated \;df = smallest\; n - 1$$ $$t=\frac{\bar{x}_1-\bar{x}_2}{ \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}$$ $$Estimated \;df = smallest\; n - 1$$